A bucket in the shape of a truncated cone is shown in the figure. The height of the bucket is 60 cm and
the radii of the top and the base are 42 cm and 28 cm respectively. Find the quantity of water it can contain,
(1 litre = 1000cm^3)
Answers
Answer:234.08litres
Step-by-step explanation:
The quantity of water the bucket which is in the shape of the cone can hold is 234.08 litre.
Step-by-step explanation:
It is given that,
The bucket is in the shape of a truncated cone i.e., a frustum of a cone whose dimensions are:
The radius of the lower base, r1 = 28 cm
The radius of the top base, r2 = 42 cm
The vertical height of the bucket, h = 60 cm
We know that,
The quantity/volume of the water that can be poured into the frustum shaped bucket will be given by,
= The volume of the frustum
= 1/3 × π × h [r1² + r2²+ (r1×r2)]
= 1/3 × (22/7) × 60 × [(28)² + (42)² + (28 × 42)]
= (440/7) × [784 + 1764 + 1176]
= (440/7) × 3724
= 234080 cm³
It is given that: 1 litre = 1000 cm³
Thus,
The quantity of water that the bucket can contain is,
= [234080 cm³] / [1000 cm^3]
= 234.08 litre
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